Decentralized Adaptive Synchronization of a Class of Discrete-Time Coupled Hidden Leader-Follower Multi-agent Systems

In this paper, the challenging problem of decentralized adaptive control for a class of coupled hidden leader-follower multi-agent systems is studied. Each agent is described by a nonlinearly parameterized uncertain model in discrete time and can receive the history information from its own neighbors. The leader agent knows the desired reference trajectory, while other agents have no access to the desired reference signal. In order to tackle unknown internal parameters and unknown high-frequency gains, a projection-type parameter estimation algorithm is presented. Using the certainty equivalence principle and neighborhood history information, the decentralized adaptive control is designed, under which the boundedness of identification error is guaranteed with the help of the Lyapunov theory. Under some conditions, the whole multi-agent system eventually achieves strong synchronization in the presence of strong couplings. A simulation example is given to support the results of the proposed scheme based on the projection-type parameter estimation algorithm. Finally, we conduct the simulations using the combination of projection and one-step-guess method, which can also achieve the strong synchronization of the whole system.